Stationarity is often a key property in the analysis of dependence structures of time series or more generally stochastic processes.
Especially stationary Gaussian processes have been extensively studied [1]}, [2]}, [3]}.
It is well known that \(\alpha \) -stable processes, where \(\alpha \in (0,2]\)  is the so-called index of stability, generalize Gaussian processes [4]}. In particular, symmetric \(\alpha \) -stable (\(S\alpha S\) ) processes are of interest.
It is the infinite second moment of \(\alpha \) -stable distributions (in the case \(\alpha <2\) ) which sets them apart from Gaussian processes (\(\alpha =2\) ), and allows them to be used for example in models of heavy-tailed random phenomena.
